If you have a home battery I'm not sure why you'd want a UPS as well?
The battery is managed based on your generation and usage patterns (eg charge up the battery from solar or overnight if grid power is cheap, discharge the battery over the evening peak when your TOU tariff is expensive). If you are worried about power outages, make sure you never discharge the battery below N kWh so you have some reserve left to run the house if the power goes out. Once you have a battery system it's a lot cheaper to add some extra kWh in batteries (using the existing inverter etc) than to buy the same in a UPS.
There's a little extra wiring in fitting a changeover switch so you can run the house in a power cut, but well worth it IMO.
Look at your power draw on your meter. If you aren't heating or cooking I expect it's going to be much less than 10kW. Even with appliances like kettles, washers and dryers going it'll be less than that.
Theo